Question

1. answer the questions for game a:

a. what is the probability of player 1 winning?
b. what is the probability of player 2 winning?
c. what is the probability of playing again?
d. is this game fair? explain your answer.

Explanation:

Part a

Step1: Identify total outcomes

When flipping two coins, the total possible outcomes (from the table) are: Heads/Heads, Heads/Tails, Tails/Heads, Tails/Tails. So there are 4 possible outcomes.

Step2: Identify favorable outcomes for Player 1

Player 1 wins only in the Heads/Heads outcome. So there is 1 favorable outcome.

Step3: Calculate probability

Probability is the number of favorable outcomes divided by total outcomes. So probability of Player 1 winning is $\frac{1}{4}$.

Step1: Identify total outcomes

As before, total outcomes are 4 (Heads/Heads, Heads/Tails, Tails/Heads, Tails/Tails).

Step2: Identify favorable outcomes for Player 2

Player 2 wins in Heads/Tails and Tails/Heads outcomes. So there are 2 favorable outcomes.

Step3: Calculate probability

Probability = number of favorable outcomes / total outcomes = $\frac{2}{4}=\frac{1}{2}$.

Step1: Identify total outcomes

Total outcomes are 4 (Heads/Heads, Heads/Tails, Tails/Heads, Tails/Tails).

Step2: Identify favorable outcomes for "Play Again"

"Play Again" occurs only in the Tails/Tails outcome. So there is 1 favorable outcome.

Step3: Calculate probability

Probability = number of favorable outcomes / total outcomes = $\frac{1}{4}$.

Answer:

$\frac{1}{4}$

Part b